Bandgap reference circuits are widely used in analog circuits for providing stable, voltage-independent, and temperature-independent reference voltages. The bandgap voltage reference circuits operate on the principle of compensating the negative temperature coefficient of a base-emitter junction voltage VBE with the positive temperature coefficient of the thermal voltage VT, with VT being equal to kT/q, wherein k is the Boltzmann constant, T is absolute temperature, and q is electron charge (1.6×10−19 coulomb). The variation of VBE with temperature at room temperature is −2.2 mV/C, while the variation of VT with temperature is +0.086 mV/C. Since VT is proportional to absolute temperature, the respective circuit portion is sometimes referred to as a PTAT circuit. Conversely, VBE is complementary to absolute temperature, and hence the respective current portion is sometimes referred to as a CTAT circuit.
As the name suggests, the voltages generated by the bandgap reference circuits are used as references, and hence the outputted reference voltages need to be highly stable. To be specific, the outputted reference voltages need to be free from temperature variation, voltage variation, and process variation. In typical bandgap reference voltage, operational amplifiers are used in order to improve the accuracy of the reference voltages. However, operational amplifiers themselves are not ideal, and have offset voltages. For example, FIG. 1 illustrates bandgap reference circuit 100, in which the offset voltage of operational amplifier 101 is represented by voltage source 102. Ideally, voltages V1 and V2 should equal each other due to the virtual short between the inputs of amplifiers. However, in practical cases, the offset voltage Vos is inevitable. Since the offset voltages Vos vary from chip to chip in a range instead of being a fixed value, the output voltages Vout also vary from chip to chip attributed to the distribution of offset voltages Vos, making it difficult to compensate for such a variation.
U.S. Pat. No. 6,690,228 discloses a bandgap reference circuit less sensitive to offset voltages of the amplifier used therein. It is realized, however, that the sensitivity of the bandgap reference circuits to the offset voltages need to be further reduced to provide more stable reference voltages.